Question: Solve for $x$ and $y$ using elimination. ${2x-3y = -24}$ ${-2x+4y = 34}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {2x-3y = -24}\thinspace$ to find $x$ ${2x - 3}{(10)}{= -24}$ $2x-30 = -24$ $2x-30{+30} = -24{+30}$ $2x = 6$ $\dfrac{2x}{{2}} = \dfrac{6}{{2}}$ ${x = 3}$ You can also plug ${y = 10}$ into $\thinspace {-2x+4y = 34}\thinspace$ and get the same answer for $x$ : ${-2x + 4}{(10)}{= 34}$ ${x = 3}$